MinT - Best Known (152−45, 152, s)-Nets in Base 4

Best Known (152−45, 152, s)-Nets in Base 4

(152−45, 152, 384)-Net over F₄ — Constructive and digital

Digital (107, 152, 384)-net over F₄, using

1 times m-reduction [i] based on digital (107, 153, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 51, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(152−45, 152, 701)-Net over F₄ — Digital

Digital (107, 152, 701)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152−45, 152, 40913)-Net in Base 4 — Upper bound on s

There is no (107, 152, 40914)-net in base 4, because

1 times m-reduction [i] would yield (107, 151, 40914)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 151671 076341 319159 114212 797996 329634 621989 847850 944720 078161 578529 481794 056025 231486 973600 > 4¹⁵¹ [i]